Show that if $f:\mathbb{C}\to\mathbb{R}$ is continuous and $f\ll1$ ($a\ll b$ means $|a|\leq |b|$), then $\int_{|z|=1}f\ll4$.
Hint: Show first $\int f\ll\int_0^{2\pi} |\sin t|dt$.
I'm not sure how to prove the hint. In addition, what does the notation of $|z|=1$ below the $\int$ sign means?